Search results for " kinetic theory"
showing 5 items of 5 documents
From the Classical Boltzmann Equation to the Generalized Kinetic models of Biological Systems
2017
This paper deal with the classical Boltzmann Equation generalized to model populations in complex biological system. In particular, the populations refer to the cells of the immune system and to those of an aggressive host (cancer cells) in a human being. We will focus with the study of a spatially homogeneous continuous model, and derivation of the macroscopic model. The paper starts from a simple description of the classical Boltzmann equation and goes to the mathematical approach proposed to model the large systems of interacting entities focusing the competition between immune system and cancer cells.
From Particle Systems to Partial Differential Equations International Conference, Particle Systems and PDEs VI, VII and VIII, 2017-2019
2021
This book includes the joint proceedings of the International Conference on Particle Systems and PDEs VI, VII and VIII. Particle Systems and PDEs VI was held in Nice, France, in November/December 2017, Particle Systems and PDEs VII was held in Palermo, Italy, in November 2018, and Particle Systems and PDEs VIII was held in Lisbon, Portugal, in December 2019. Most of the papers are dealing with mathematical problems motivated by different applications in physics, engineering, economics, chemistry and biology. They illustrate methods and topics in the study of particle systems and PDEs and their relation. The book is recommended to probabilists, analysts and to those mathematicians in general…
Self-consistent calculation of the flux-flow conductivity in diffusive superconductors
2017
In the framework of Keldysh-Usadel kinetic theory, we study the temperature dependence of flux-flow conductivity (FFC) in diffusive superconductors. By using self-consistent vortex solutions we find the exact values of dimensionless parameters that determine the diffusion-controlled FFC both in the limit of the low temperatures and close to the critical one. Taking into account the electron-phonon scattering, we study the transition between flux-flow regimes controlled by either the diffusion or the inelastic relaxation of nonequilibrium quasiparticles. We demonstrate that the inelastic electron-phonon relaxation leads to the strong suppression of FFC compared to the previous estimates, mak…
Self-consistent calculation of the flux-flow conductivity in diffusive superconductors
2017
In the framework of Keldysh-Usadel kinetic theory, we study the temperature dependence of flux-flow conductivity (FFC) in diffusive superconductors. By using self-consistent vortex solutions we find the exact values of dimensionless parameters that determine the diffusion-controlled FFC both in the limit of the low temperatures and close to the critical one. Taking into account the electron-phonon scattering we study the transition between flux-flow regimes controlled either by the diffusion or the inelastic relaxation of non-equilibrium quasiparticles. We demonstrate that the inelastic electron-phonon relaxation leads to the strong suppression of FFC as compared to the previous estimates m…
On the modeling of nonlinear interactions in large complex systems
2010
Abstract This work deals with the modeling of large systems of interacting entities in the framework of the mathematical kinetic theory for active particles. The contents are specifically focused on the modeling of nonlinear interactions which is one of the most important issues in the mathematical approach to modeling and simulating complex systems, and which includes a learning–hiding dynamics. Applications are focused on the modeling of complex biological systems and on immune competition.